Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Velocity Distribution in Smooth Rectangular Open Channels-Closure

Abstract is not available.

Lower Bound Limit Analysis of Rectangular Slabs

A general method for the development of valid lower bound solutions to uniformly distributed and orthotropically reinforced rectangular concrete slabs obeying normal moment criterion is described. General expressions for moment field have been obtained for nine cases of slabs having all combinations of simply supported and clamped-edge conditions. The lower bound collapse loads have been compared with the upper bound values obtained by the yield line theory. The paper also focuses attention to the need for the development of valid upper bound solutions with the satisfaction of kinematical admissibility and the flow rules associated with the normal moment criterion.

Free vibration of rectangular plates of arbitrary thickness

Free vibration of thick rectangular plates is investigated by using the “method of initial functions” proposed by Vlasov. The governing equations are derived from the three-dimensional elastodynamic equations. They are obtained in the form of series and theories of any desired order can be constructed by deleting higher terms in the infinite order differential equations. The numerical results are compared with those of classical, Mindlin, and Lee and Reismann solutions.

Dielectric-lined rectangular metal waveguide

The propagation characteristics of electromagnetic waves in a dielectric-lined rectangular metal waveguide have been studied. The lining on the two side walls (E-plane) together with the air space in between them is considered as a homogeneous equivalent dielectric medium whose equivalent dielectric constant is derived by using electrostatic theory. The theoretical work is based on the fact that LSE and LSM modes can be propagated in a rectangular metal waveguide lined in the two longer sides (H-plane) by dielectric lining. Experimental verification of the guide wavelength at 'X', 'ku' and 'Ka' bands and cut-off frequency are reported.

Free vibration of rectangular plates of arbitrary thickness with one or more edges clamped

Frequencies of free vibration of rectangular plates of arbitrary thickness, with different support conditions, are calculated by using the Method of Initial Functions (MIF), proposed by Vlasov. Sixth and fourth order MIF theories are used for the solution. Numerical results are presented for three square plates for three thickness ratios. The support conditions considered are (i) three sides simply supported and one side clamped, (ii) two opposite sides simply supported and the other two sides clamped and (iii) all sides clamped. It is found that the results produced by the MIF method are in fair agreement with those obtained by using other methods. The classical theory gives overestimates of the frequencies and the departures from the MIF results increase for higher modes and larger thickness ratios.

Anion directed template synthesis of Cu(II) complexes of a N,N,O donor mono-condensed Schiff base ligand: A molecular scaffold forming highly ordered H-bonded rectangular grids

Anion directed, template syntheses of two dinuclear copper(II) complexes of mono-condensed Schiff base ligand Hdipn (4-[(3-aminopentylimino)-methyl]-benzene-1,3-diol) involving 2,4- dihydroxybenzaldehyde and 1,3-diaminopentane were realized in the presence of bridging azide and acetate anions. Both complexes, [Cu-2(dipn)(2)(N-3)(2)] (1) and [Cu-2(dip(n))(2)(OAc)(2)] (2) have been characterized by X-ray crystallography. The two mononuclear units are joined together by basal-apical, double end-on azido bridges in complex 1 and by basal-apical, double mono-atomic acetate oxygen-bridges in 2. Both complexes form rectangular grid-like supramolecular structures via H-bonds connecting the azide or acetate anion and the p-hydroxy group of 2,4- dihydroxybenzaldehyde. Variable-temperature (300-2 K) magnetic susceptibility measurements reveal that complex 1 has antiferromagnetic coupling (J = -2.10 cm (1)) through the azide bridge while 2 has intra-dimer ferromagnetic coupling through the acetate bridge and inter-dimer antiferromagnetic coupling through H-bonds (J = 2.85 cm (1), J' = -1.08 cm (1)). (C) 2009 Elsevier B. V. All rights reserved.

Experimental Demonstration of H{infty} Control based Active Vibration Suppression in Composite Fin-tip of Aircraft using Optimally Placed Piezoelectric Patch Actuators

The goal of this study is the multi-mode structural vibration control in the composite fin-tip of an aircraft. Structural model of the composite fin-tip with surface bonded piezoelectric actuators is developed using the finite element method. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes accurately. A model order reduction technique is employed for reducing the finite element structural matrices before developing the controller. Particle swarm based evolutionary optimization technique is used for optimal placement of piezoelectric patch actuators and accelerometer sensors to suppress vibration. H{infty} based active vibration controllers are designed directly in the discrete domain and implemented using dSpace® (DS-1005) electronic signal processing boards. Significant vibration suppression in the multiple bending modes of interest is experimentally demonstrated for sinusoidal and band limited white noise forcing functions.

Stress concentration and load diffusion in rectangular panels with constant stress flanges

The stress concentration that occurs when load is diffused from a constant stress member into thin sheet is an important problem in the design of light weight structures. By using solutions in biharmonic polar-trigonometric series, the stress concentration can be effectively isolated so that highly accurate information necessary for design can be obtained. A method of analysis yielding high accuracy with limited effort is presented for rectangular panels with transverse edges free or supported by inextensional end ribs. Numerical data are given for panels with length twice the width.

Large deflections of rectangular plates

Approximate solutions for the non-linear bending of thin rectangular plates are presented considering large deflections for various boundary conditions. In the case of stress-free edges, solutions are given for von Kármán's equations in terms of the stress function and the deflection of the plate. In the case of immovable edges, equations are constructed in terms of the three displacements and these are solved. The solution is given by using double series consisting of the appropriate Beam Functions which satisfy the boundary conditions. The differential equations are satisfied by using the orthogonality properties of the series. Numerical results for square plates with uniform lateral load indicate good convergence of the series solution presented here.

Thermal stresses in rectangular plates

A method of determining the thermal stresses in a flat rectangular isotropic plate of constant thickness with arbitrary temperature distribution in the plane of the plate and with no variation in temperature through the thickness is presented. The thermal stress have been obtained in terms of Fourier series and integrals that satisfy the differential equation and the boundary conditions. Several examples have been presented to show the application of the method.

Design of rectangular reinforced concrete slabs supported on all the sides with a short discontinuous edge

Bending moment coefficients for the design of rectangular reinforced concrete panels supported on four sides with a short discontinuous edge are derived using the strip theory. The moment fields resulting from the use of proposed coefficients are examined in terms of the moment volume for possible savings in reinforcement and compared with other codified procedures. The strip coefficients averaged over the corresponding sides of the panel, besides resulting in considerable savings in reinforcement, are found to be identical with the coefficients predicted by simple yield line theory using an orthotropic layout of reinforcement.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Vibration of rectangular orthotropic plates

An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate. Nomenclature 2a, 2b sides of the rectangular plate h plate thickness Eprime x , Eprime y , EPrime, G elastic constants of te orthotropic material D x Eprime x h 3/12 D y Eprime y h 3/12 H xy EPrimeh 3/12+Gh 3/6 D x , D y and H xy are rigidity constants of the orthotropic platergr mass of the plate per unit area ngr Poisson's ratio W deflection of the plate p circular frequency gamma b/a ratio X m , Y characteristic functions of the vibrating beam problem -lambda rgrp 2 a 2 b 2/H xy the frequency parameter.